Methods for Estimating Mechanical Properties from Magnetic Resonance Elastography Data  Using Artificial Neural Networks

ABSTRACT

Described here are systems and methods for magnetic resonance elastography (“MRE”), or other imaging-based elastography techniques, in which a machine learning approach, such as an artificial neural network, is implemented to perform an inversion of displacement data in order to generate estimates of the mechanical properties, such as stiffness and damping ratio, of tissues in a subject.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional PatentApplication Ser. No. 62/588,115, filed on Nov. 17, 2017, and entitled“METHODS FOR ESTIMATING TISSUE STIFFNESS FROM MAGNETIC RESONANCEELASTOGRAPHY DATA USING ARTIFICIAL NEURAL NETWORKS,” which is hereinincorporated by reference in its entirety.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH

This invention was made with government support under EB001981 awardedby the National Institutes of Health. The government has certain rightsin the invention.

BACKGROUND

Magnetic resonance elastography (“MRE”) is a magnetic resonance imaging(“MRI”)-based technique for measuring tissue stiffness, akin to manualpalpation, which has a long history in the practice of medicine. MREincludes introducing shear waves into a tissue-of-interest by mechanicalvibration. Next, the resulting tissue displacement is imaged by aphase-contrast MRI pulse sequence with motion encoding gradients thatare synchronized to the motion. Finally, these displacement images aremathematically inverted to calculate tissue stiffness.

MRE is growing in clinical impact, particularly for applications in theliver, where it is used to noninvasively assess fibrosis with highaccuracy. Furthermore, brain stiffness has shown sensitivity to a numberof physiological processes including neurodegenerative disease, normalaging, and even behavioral performance. Still, there remains amotivation to improve the effective resolution and robustness of MRE toenable further investigation into the spatial relationship betweentissue mechanical properties and pathophysiology, and to open up newapplications in focal diseases.

Elastography can also be performed with other imaging modalities, suchas ultrasound and some optical techniques. Many of these elastographytechniques are similar to MRE in the sense that shear waves areintroduced into the tissue, or material, and the resulting displacementsare measured by the imaging modality. To this end, the inversionalgorithms used to compute stiffness and other mechanical propertiesfrom these displacement data, and the issues facing such algorithms, aresimilar to those faced in MRE.

Currently, the inversion algorithms used to compute stiffness from thedisplacement data represent one of the greatest limitations on theresolution of MRE and other elastography techniques. A number of methodsexist for performing the inversion calculation, each with its unique setof advantages and disadvantages. Popular algorithms in the fieldinclude, but are not limited to, variations of direct inversion (“DI”),local frequency estimation, and non-linear inversion. Each model relieson underlying assumptions that will impact its performance in in vivodata, as well as a number of implementation choices (e.g., tuningparameters and filter settings) that affect the tradeoff betweenresolution and numerical stability. An algorithm that can provide stableestimates in the presence of noise while maintaining a small spatialfiltering footprint could substantially improve the effective resolutionof MRE and other elastography techniques, either by mitigating the needfor smoothing or by allowing reliable estimation in smaller regions.

SUMMARY OF THE DISCLOSURE

The present disclosure addresses the aforementioned drawbacks byproviding a method for generating an image that depicts a mechanicalproperty in a tissue of a subject. Displacement data are provided to acomputer system, the displacement data having been acquired with amagnetic resonance imaging (“MRI”) system and depicting displacementscaused in a subject by vibratory motion applied to the subject while thesubject was imaged with the MRI system. Training data representative ofthe displacement data are also provided to the computer system. A neuralnetwork is constructed and trained on the training data using thecomputer system. An image that depicts a mechanical property in a tissueof the subject is generated by inputting the displacement data to thetrained neural network.

The foregoing and other aspects and advantages of the present disclosurewill appear from the following description. In the description,reference is made to the accompanying drawings that form a part hereof,and in which there is shown by way of illustration a preferredembodiment. This embodiment does not necessarily represent the fullscope of the invention, however, and reference is therefore made to theclaims and herein for interpreting the scope of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of an example neuron.

FIG. 2 is an example of a model neuron used in an artificial neuralnetwork, which computes the sum of the product of weights, w, andinputs, x, as well as a bias term, and then applies a nonlinear transferfunction, h.

FIG. 3 is a diagram of an example feedforward neural network with threeinputs, two hidden layers with five units in each, and a single output.

FIG. 4 is a flowchart setting forth the steps of an example method forgenerating a mechanical property map using magnetic resonanceelastography (“MRE”), or another suitable elastography technique, toprovide displacement data that are input to an artificial neural networktrained to implement elastography inversion.

FIG. 5 is a block diagram of an example system that can implement amechanical property estimation system as described in the presentdisclosure.

FIG. 6 is a block diagram of example hardware components that canimplement the system of FIG. 5.

FIG. 7 is a block diagram of an example magnetic resonance imaging(“MRI”) system that can implement the methods described in the presentdisclosure.

DETAILED DESCRIPTION

Described here are systems and methods for magnetic resonanceelastography (“MRE”), and other elastography techniques, in which amachine learning approach, such as an artificial neural network, isimplemented to perform an inversion of displacement data in order togenerate estimates of the mechanical properties of a subject. Usingmachine learning to implement inversion (e.g., MRE inversion) isadvantageous because it is data-driven, and thus provides a frameworkfor dealing with practical issues such as tissue inhomogeneity, partialvolume effects, and noise. Moreover, predictions made from these modelsare effectively bounded by the training data, and thus provide stabilitywhen measuring stiffness in smaller regions.

As will be described, the systems and methods described in the presentdisclosure provide for the inversion of displacement data in a mannerthat provides stable mechanical property (e.g., stiffness, dampingratio) estimates in the presence of noise, does not require assumptionson local homogeneity, is computationally efficient when compared withprevious inversion techniques, and is capable of inverting displacementdata acquired at a single frequency, or at multiple frequencies.

Although other machine learning approaches can be implemented,artificial neural networks (“ANNs”) have an advantage where the optimalpreprocessing of the displacement data in order to estimate stiffness isnot necessarily known ahead of time. ANNs with multiple hidden layersare capable of learning abstract representations of the inputs, whichcan then be utilized by deeper layers to estimate the quantity ofinterest. One non-limiting example of machine learning algorithms otherthan ANNs that can implement the methods described in the presentdisclosure include trained reaction diffusion networks.

ANNs represent a class of function approximators inspired by neuralnetworks found in the brain. A simple model of a neuron is shown inFIG. 1. Upstream neurons form synapses with this cell in the dendritictree, where the release of neurotransmitters will open ion channels andalter the membrane potential at the synaptic site. These electricalsignals then passively propagate through the cell body to the axonhillock, where a decision is made about whether to generate an outputsignal (i.e., an action potential). Notably, upstream neurons havevarying degrees of influence on this decision at the hillock dependingon the distance to that particular synapse and the conduction propertiesof the dendritic tree along that path. If these postsynaptic potentialssum to a certain threshold potential, then voltage-gated ion channelswill be opened at the hillock initiating the formation of an actionpotential. An action potential is a large spike in the membranepotential of the cell, which is propagated down the axon to initiateneurotransmitter release at the synaptic terminal, and thus influencethe membrane potential of the downstream neuron.

A schematic representation of a neuron is shown in FIG. 2 for thepurpose of understanding the ANNs described in the present disclosure.The properties of this model neuron are that it first computes theweighted sum of input from upstream neurons (x) as well as a bias term(b), and then applies a nonlinear transfer function, h(x), to thisvalue, and then sends this output to downstream neurons. As onenon-limiting example, the transfer function, h(x), can be a hyperbolictangent transfer function (also called an activation function), thoughseveral other candidate functions can also be readily implemented. Forexample, a rectified linear unit (“RELU”) action function could also beused.

One example of an ANN architecture that can be implemented by themethods described in the present disclosure is a feedforward neuralnetwork with fully-connected layers. An example feedforward ANN is shownin FIG. 3. This example feedforward ANN has three inputs 302 (orfeatures), two hidden layers 304 with five neurons in each hidden layer304, and a single neuron in the output layer 306. In this type of ANN,each neuron receives input from every neuron in the previous layer, andsends its output to every neuron in the following layer. Each of theseneurons can operate as the model shown in FIG. 2. In another example,the ANN can include more than two hidden layers (e.g., three or morehidden layers) and each hidden layer can contain fewer than, or morethan, five neurons. The ANN can also include other layers in addition tothe two or more hidden layers. For instance, the ANN could includeconvolutional layers, activation or nonlinear layers, dropout layers,pooling layers (e.g., max pooling layers), and so on. One or more of thelayers in the ANN may be fully connected layers.

The weights of the ANN are learned through a training process. As onenon-limiting example of a training process, in the case of supervisedtraining, the weights are adjusted iteratively by a backpropagationmethod (e.g., a scaled gradient backpropagation or other backpropagationtechnique) using a training set that contains features and known desiredoutputs. In this example, the weights are initialized with small, randomvalues. Then, the ANN is evaluated in the forward direction and theerror is calculated between the ANN prediction and the known targetvalues provided by the training set. Next, the gradient of the errorwith respect to each weight is computed in the backward direction,beginning with the output layer and working progressively upstream, eachtime using the previously computed gradients to calculate errors in theimmediately upstream-layer according to the chain rule. With the errorand gradients computed, any one of a number of nonlinear optimizationalgorithms can be used to update the weights for the next iteration.This process is repeated until a stopping criterion is reached. As oneexample, training can be stopped when the error is no longer reduced ina separate cross-validation set, such as when mean squared error is notimproved in the validation set for a number of consecutive iterations.

Referring now to FIG. 4, a flowchart is illustrated as setting forth thesteps of an example method for generating images that depict mechanicalproperties in a subject by performing inversion (e.g., MRE inversion) ondisplacement data using an artificial neural network. Examples ofmechanical properties that can be estimated using the methods describedin the present disclosure include, but are not limited to, stiffness,storage modulus, loss modulus, damping ratio, poroelastic parameters,and so on. In some instances, the systems and methods described in thepresent disclosure can implement neural networks that are trained toestimate mechanical properties from more complicated rheological models(e.g., a Voigt model, poroelastic models, anisotropic models).

The method includes providing displacement data to a computer system, asindicated at step 402. The displacement data can include, for instance,wave images obtained using an MRE scan. The displacement data may beprovided to the computer system by retrieving previously acquireddisplacement data from a memory or other suitable data storage. Asanother example, the displacement data may be provided to the computersystem by acquiring displacement data using an MRI system that is incommunication with the computer system. In some instances, the computersystem may form a part of the MRI system. Such displacement data can beacquired by operating the MRI system to perform an MRE scan, such asthose described in U.S. Pat. No. 5,592,085, which is herein incorporatedby reference in its entirety. In still other embodiments, thedisplacement data can be obtained with other imaging modalities andtechniques. For instance, the elastography data could be obtained usingultrasound elastography techniques or optical elastography techniques.

In general, the displacement data are representative of displacementsoccurring in the subject while the displacement data are acquired. Insome instances, the displacement data may be representative oftime-harmonic displacement fields. In some other instances, thedisplacement data may be representative of transient displacementfields.

The displacement data may represent displacements caused by a singlewave source, or by multiple wave sources. More generally, thedisplacement data may represent displacements associated with a singlewave field or with multiple wave fields. In some instances, thedisplacement data can represent simultaneous, multifrequencydisplacement.

A neural network is trained, as generally indicated at process block404. In general, the neural network is trained on training data, whichmay be simulated data, displacement data acquired from a previousimaging session (e.g., a previous MRE scan), or some or all of thedisplacement data provided in step 402.

Thus, the training process can include providing suitable training data,as indicated at step 406. As mentioned, in some embodiments, the neuralnetwork can be trained on simulated data. For instance, simulated datacan include patches of voxels containing simulated displacement datahaving a number of different phase offsets over one or more periods ofmotion. The patches may be one-dimensional, two-dimensional, orthree-dimensional. As one non-limiting example, the simulated data caninclude 5×5 patches with 2-mm isotropic voxels and 4 phase offsetsspaced evenly over one period of 60-Hz motion. Other patch sizes canalso be implemented, such as 3×3, 7×7, 11×11, and soon.Three-dimensional patches can also be used, such as 5×5×5 sized patches.In some instances, the patch sizes are not symmetrical, such as patcheswith sizes m×n, m×m×n, m×n×p, or otherwise, where m≠n≠p. Voxel sizesother than 2-mm, whether isotropic or otherwise, can also be used. Thestiffness values used for the simulated data can be chosen randomly. Asan example, the stiffness values can be chosen randomly from a uniformdistribution with a range of values, such as 0.1 to 10 kPa.

The simulated data can be generated using a simulation in which a singlepoint-source is placed in a random location at a randomly assigneddistance from the center of the patch. In some other instances, thesimulated data can be generated using a simulation in which one or morepoint-sources are placed in random locations within a patch. Previousinversion techniques have difficulty estimating mechanical propertiesnear wave sources; however, it is contemplated that the systems andmethods described in the present disclosure can overcome thesechallenges and provide estimation of mechanical properties even nearwave sources. A sinusoidal wave can be computed as a function ofdistance from that source to produce radially propagating waves with theappropriate wavelength attenuation. In other examples, multiple wavesources can be used. For instance, a random number of sources can eachbe placed at a random location within a simulation region. In theseexamples, the simulated displacements can be computed as thesuperposition of the multiple sources divided by the number of sources.

As one non-limiting example, the training data may include simulationdata generated using a coupled harmonic oscillators (“CHO”) simulation;however, other simulation techniques may also be used, including finiteelement models, finite difference models, and so on. Such simulationdata may include a number of 2D data sets, 3D data sets, or combinationsthereof. For instance, the simulation data may include 2D data sets thateach include a patch of isotropic pixels or non-isotropic pixels.Advantageously, CHO simulations can be used to generate simulation datafor displacement in an inhomogeneous medium.

In one example implementation, 70×70 patches with 2-mm isotropic pixelswith a homogeneous background and an inclusion ranging in diameter from1-10 cm placed in the center of the patch were used. In such examples,the stiffness of the background and the inclusion in each patch can bechosen randomly from a distribution, such as a uniform distribution from1-10 kPa. In the example of using a CHO simulation to generatesimulation data, a randomly selected number of harmonic force generators(e.g., 1-10) with an oscillation frequency (e.g., 100 Hz) can be placedat the boundary of the simulation. For instance, in someimplementations, the simulation data can be generated to representmotion-type information around the boundaries of a region in order toestimate the properties of what is inside the region.

Damping can be assumed constant across all simulation, and can beassumed to be homogeneous within each simulation. In otherimplementations, however, the damping can be variable, inhomogeneousacross each simulation, or both. The level of damping can be selectedsuch that the wave from a single point source would travel across theentire simulation footprint before complete attenuation. Other levels ofdamping can also be selected as desired. As one example, a steady-statesolution at four phase offsets equally distributed across one period ofmotion can be used to generate four displacement images for each dataset.

In some embodiments, the training data can be augmented. For instance,some or all of the patches in the training data can be adjusted,manipulated, or otherwise processed. For example, patches from randomlyselected locations can be further adjusted, manipulated, or processed.As one example, patches from randomly selected locations centered anumber of pixels (e.g., one pixel) adjacent to the boundary of theinclusion, or on the boundary itself, can be selected. The selectedpatches can be rotated. For instance, the selected patches can each berotated by a random number of degrees. As one example, the selectedpatches can each be rotated by a random multiple of 90 degrees. Otherdata augmentations, such as horizontal flips, vertical flips, randomcrops, translations, and so on, can also be implemented.

In some instances, noise can be added to the simulated data. Forexample, randomly chosen signal-to-noise ratio (“SNR”) values can beselected from a distribution of such values, such as a uniformdistribution in a range of 1 to 20. The noise may be pseudorandom noisewith a Gaussian distribution, or other suitable forms of noise. Thenoise may have a zero mean, and may have a standard deviation that isscaled to provide the prescribed SNR values. The noise can be added tothe simulated data.

As another example, the noise added to the simulated data may bestructured to be more representative of noise commonly encountered inMRI. In these examples, the simulated displacements can be convertedinto system-specific and MRE sequence-specific phase values using MREsignal encoding models. This phase signal can then be additivelycombined with a synthetic low-order phase field that simulatessusceptibility effects. A complex image can be generated using thissimulated phase and a magnitude signal, which may be either ananatomical image or anatomically realistic binary mask. Finally, zeromean proper complex Gaussian noise can be added to this image. TheMR-realistic MRE displacement image can be obtained using standardprocessing tools, such as phase differencing of images simulated withpositive/negative motion encoding gradient pairs. The fundamental noiselevel (e.g., variance of complex Gaussian noise) for each trainingexample can be assigned randomly from a uniform distribution with arange chosen to sufficiently stratify an expected range of magnitudeSNRs, which may be measured from previous studies. Adding noise in thismanner ensures that the simulated training data are statisticallyconsistent with the MRI-based data which are later inputted to theneural network.

In some instances, the training data may include missing data. As anexample, the training data may include patches of displacement datawhich are masked to remove some of the displacement data. For instance,randomly selected mask patches can be applied to patches of displacementdata in order to generate masked displacement data patches. The maskpatches can be selected from the acquired data, as an example. In suchinstances, the mask patches are preferably selected so as not to crossmajor anatomical boundaries. In the case of brain imaging, the maskpatches can be selected so as not to cross boundaries such as the falxcerebri, the tentorium cerebelli, the Sylvian fissure, and the like.

The training process also includes providing the neural network to betrained, as indicated at step 408. Providing the neural network caninclude selecting the type of neural network and the correspondingparameters of that neural network. For instance, the neural network maybe a feedforward neural network, a convolutional neural network, orother type of neural network. For instance, in some implementations theneural network may implement a variational sparse coding network or aconvolutional sparse coding network. Parameters that can be selectedinclude the types and numbers of layers, as well as the number ofneurons in each layer, and so on.

The neural network is then trained on the provided training data, asindicated at step 410. Training can be performed on features extractedfrom the training data. For instance, the features given to the modelfor each observation, x_(i), can include the real and imaginary parts ofa temporal harmonic, such as the first temporal harmonic, of thedisplacement data in each patch of simulated data. In otherimplementations, the neural network can be trained directly oncomplex-valued data, rather than data with real and imaginary partsdecoupled. In such instances, a phase-preserving complex transferfunction can be used. The features can also be linearly scaled such thatthe range of ±|x_(i)| is mapped to the range −1 to +1. In still otherimplementations, the neural network can be trained directly on timeoffsets without computing the first temporal harmonic. As one example,the neural network model can be trained by fitting the training data tothe neural network model a backpropagation technique, such as a scaledconjugate gradient backpropagation. As another example, the neuralnetwork can be trained using a stochastic optimization (e.g., astochastic gradient descent). In some implementations, variancereduction setups, such as stochastic average gradient, can also be used.In some implementations, the training data are processed and the neuralnetwork is trained on the processed training data. As one example, thetraining data can be projected onto a basis before training.

A determination is made at decision block 412 whether a stoppingcriterion has been satisfied. If not, then another iteration of trainingthe neural network occurs; otherwise, the trained neural network isstored, as indicated at step 414, for later use.

After the neural network is trained, the provided displacement data areinput to the trained neural network to generate one or more mechanicalproperty maps, as indicated at step 416. The mechanical property mapscan include, for example, stiffness maps that provide quantitativeinformation about the stiffness of tissues in the subject from which thedisplacement data were acquired. The mechanical property maps can alsoinclude, for example, damping ratio maps that provide quantitativeinformation about the damping ratio of tissues in the subject from whichthe displacement data were acquired. Mechanical property maps aregenerated, for instance, by evaluating the trained neural network ateach voxel in the displacement data.

As an example, the displacement data are input to one or more inputunits in an input layer of the trained neural network, generatingoutput. The output from the input layer is passed to a first hiddenlayer, generating output. The output of this hidden layers is thenpassed to the next hidden layer, generating output. This process isrepeated for the number of hidden layers in the neural network. Theoutput generated by the last hidden layer includes the one or moremechanical property maps.

In some embodiments, the displacement data can be processed before beinginput to the trained neural network. For example, the displacement datacan have phase unwrapping applied, can have background phase removed,and can be directional filtered.

In some other embodiments, the displacement data are processed toproduce different data that are input into the neural network. Forexample, edge-aware methods can be used to compute the curl on thedisplacement data, and the curl data can then be smoothed, such as witha quartic kernel without using data from outside the prescribed ROI.Mechanical property maps can then be computed by evaluating a trainedneural network in every voxel using the first temporal harmonic of thecurl as the inputs to the trained ANN. In these instances, the neuralnetwork can be trained on patches of curl data. The three components ofthe displacements, or of the curl of the displacement, can be invertedseparately and then combined into a single mechanical property map (e.g.stiffness map) by computing the weighted average using the squaredamplitude of each component.

Referring now to FIG. 5, an example of a system 500 for generatingmechanical property maps, or otherwise estimating mechanical properties,in accordance with some embodiments of the systems and methods describedin the present disclosure is shown. As shown in FIG. 5, a computingdevice 550 can receive one or more types of data (e.g., displacementdata, magnetic resonance image data) from image data source 502, whichmay be source of magnetic resonance images, displacement data acquiredwith an MRI system, displacement data acquired with an ultrasoundsystem, displacement data acquired with an optical elastographytechnique, and so on. In some embodiments, computing device 550 canexecute at least a portion of a mechanical property estimation system504 to generate mechanical property maps, or otherwise or predictmechanical properties, from data received from the image data source502.

Additionally or alternatively, in some embodiments, the computing device550 can communicate information about data received from the image datasource 502 to a server 552 over a communication network 554, which canexecute at least a portion of the mechanical property estimation system504 to generate mechanical property maps, or otherwise or predictmechanical properties, from data received from the image data source502. In such embodiments, the server 552 can return information to thecomputing device 550 (and/or any other suitable computing device)indicative of an output of the mechanical property estimation system 504to generate mechanical property maps, or otherwise or predict mechanicalproperties, from data received from the image data source 502. In someaspects, the mechanical property estimation system 504 may implementconstructing a neural network (e.g., selecting a type of neural network;selecting a number and type of layers; selecting a number of inputs;selecting weights, biases, transfer functions, or other parameters forone or more layers), training the neural network on training data, andgenerating mechanical property maps by inputting displacement data orother suitable data to the trained neural network.

In some embodiments, computing device 550 and/or server 552 can be anysuitable computing device or combination of devices, such as a desktopcomputer, a laptop computer, a smartphone, a tablet computer, a wearablecomputer, a server computer, a virtual machine being executed by aphysical computing device, and so on. The computing device 550 and/orserver 552 can also reconstruct images from the data.

In some embodiments, image data source 502 can be any suitable source ofimage data (e.g., measurement data, images reconstructed frommeasurement data, displacement data), such as an MRI system, anultrasound system, an optical imaging system, another computing device(e.g., a server storing image data, displacement data, or both), and soon. In some embodiments, image data source 502 can be local to computingdevice 550. For example, image data source 502 can be incorporated withcomputing device 550 (e.g., computing device 550 can be configured aspart of a device for capturing, scanning, and/or storing images). Asanother example, image data source 502 can be connected to computingdevice 550 by a cable, a direct wireless link, and so on. Additionallyor alternatively, in some embodiments, image data source 502 can belocated locally and/or remotely from computing device 550, and cancommunicate data to computing device 550 (and/or server 552) via acommunication network (e.g., communication network 554).

In some embodiments, communication network 554 can be any suitablecommunication network or combination of communication networks. Forexample, communication network 554 can include a Wi-Fi network (whichcan include one or more wireless routers, one or more switches, etc.), apeer-to-peer network (e.g., a Bluetooth network), a cellular network(e.g., a 3G network, a 4G network, etc., complying with any suitablestandard, such as CD MA, GSM, LTE, LTE Advanced, WiMAX, etc.), a wirednetwork, and so on. In some embodiments, communication network 108 canbe a local area network, a wide area network, a public network (e.g.,the Internet), a private or semi-private network (e.g., a corporate oruniversity intranet), any other suitable type of network, or anysuitable combination of networks. Communications links shown in FIG. 5can each be any suitable communications link or combination ofcommunications links, such as wired links, fiber optic links, Wi-Filinks, Bluetooth links, cellular links, and so on.

Referring now to FIG. 6, an example of hardware 600 that can be used toimplement image data source 502, computing device 550, and server 554 inaccordance with some embodiments of the systems and methods described inthe present disclosure is shown. As shown in FIG. 6, in someembodiments, computing device 550 can include a processor 602, a display604, one or more inputs 606, one or more communication systems 608,and/or memory 610. In some embodiments, processor 602 can be anysuitable hardware processor or combination of processors, such as acentral processing unit (“CPU”), a graphics processing unit (“GPU”), andso on. In some embodiments, display 604 can include any suitable displaydevices, such as a computer monitor, a touchscreen, a television, and soon. In some embodiments, inputs 606 can include any suitable inputdevices and/or sensors that can be used to receive user input, such as akeyboard, a mouse, a touchscreen, a microphone, and so on.

In some embodiments, communications systems 608 can include any suitablehardware, firmware, and/or software for communicating information overcommunication network 554 and/or any other suitable communicationnetworks. For example, communications systems 608 can include one ormore transceivers, one or more communication chips and/or chip sets, andso on. In a more particular example, communications systems 608 caninclude hardware, firmware and/or software that can be used to establisha Wi-Fi connection, a Bluetooth connection, a cellular connection, anEthernet connection, and so on.

In some embodiments, memory 610 can include any suitable storage deviceor devices that can be used to store instructions, values, data, or thelike, that can be used, for example, by processor 602 to present contentusing display 604, to communicate with server 552 via communicationssystem(s) 608, and so on. Memory 610 can include any suitable volatilememory, non-volatile memory, storage, or any suitable combinationthereof. For example, memory 610 can include RAM, ROM, EEPROM, one ormore flash drives, one or more hard disks, one or more solid statedrives, one or more optical drives, and so on. In some embodiments,memory 610 can have encoded thereon, or otherwise stored therein, acomputer program for controlling operation of computing device 550. Insuch embodiments, processor 602 can execute at least a portion of thecomputer program to present content (e.g., images, user interfaces,graphics, tables), receive content from server 552, transmit informationto server 552, and so on.

In some embodiments, server 552 can include a processor 612, a display614, one or more inputs 616, one or more communications systems 618,and/or memory 620. In some embodiments, processor 612 can be anysuitable hardware processor or combination of processors, such as a CPU,a GPU, and so on. In some embodiments, display 614 can include anysuitable display devices, such as a computer monitor, a touchscreen, atelevision, and so on. In some embodiments, inputs 616 can include anysuitable input devices and/or sensors that can be used to receive userinput, such as a keyboard, a mouse, a touchscreen, a microphone, and soon.

In some embodiments, communications systems 618 can include any suitablehardware, firmware, and/or software for communicating information overcommunication network 554 and/or any other suitable communicationnetworks. For example, communications systems 618 can include one ormore transceivers, one or more communication chips and/or chip sets, andso on. In a more particular example, communications systems 618 caninclude hardware, firmware and/or software that can be used to establisha Wi-Fi connection, a Bluetooth connection, a cellular connection, anEthernet connection, and so on.

In some embodiments, memory 620 can include any suitable storage deviceor devices that can be used to store instructions, values, data, or thelike, that can be used, for example, by processor 612 to present contentusing display 614, to communicate with one or more computing devices550, and so on. Memory 620 can include any suitable volatile memory,non-volatile memory, storage, or any suitable combination thereof. Forexample, memory 620 can include RAM, ROM, EEPROM, one or more flashdrives, one or more hard disks, one or more solid state drives, one ormore optical drives, and so on. In some embodiments, memory 620 can haveencoded thereon a server program for controlling operation of server552. In such embodiments, processor 612 can execute at least a portionof the server program to transmit information and/or content (e.g.,data, images, a user interface) to one or more computing devices 550,receive information and/or content from one or more computing devices550, receive instructions from one or more devices (e.g., a personalcomputer, a laptop computer, a tablet computer, a smartphone), and soon.

In some embodiments, image data source 502 can include a processor 622,one or more image acquisition systems 624, one or more communicationssystems 626, and/or memory 628. In some embodiments, processor 622 canbe any suitable hardware processor or combination of processors, such asa CPU, a GPU, and so on. In some embodiments, the one or more imageacquisition systems 624 are generally configured to acquire data,images, or both, and can include an MRI system, an ultrasound system, oran optical imaging system. Additionally or alternatively, in someembodiments, one or more image acquisition systems 624 can include anysuitable hardware, firmware, and/or software for coupling to and/orcontrolling operations of an MRI system, an ultrasound system, or anoptical imaging system. In some embodiments, one or more portions of theone or more image acquisition systems 624 can be removable and/orreplaceable.

Note that, although not shown, image data source 502 can include anysuitable inputs and/or outputs. For example, image data source 502 caninclude input devices and/or sensors that can be used to receive userinput, such as a keyboard, a mouse, a touchscreen, a microphone, atrackpad, a trackball, and so on. As another example, image data source502 can include any suitable display devices, such as a computermonitor, a touchscreen, a television, etc., one or more speakers, and soon.

In some embodiments, communications systems 626 can include any suitablehardware, firmware, and/or software for communicating information tocomputing device 550 (and, in some embodiments, over communicationnetwork 554 and/or any other suitable communication networks). Forexample, communications systems 626 can include one or moretransceivers, one or more communication chips and/or chip sets, and soon. In a more particular example, communications systems 626 can includehardware, firmware and/or software that can be used to establish a wiredconnection using any suitable port and/or communication standard (e.g.,VGA, DVI video, USB, RS-232, etc.), Wi-Fi connection, a Bluetoothconnection, a cellular connection, an Ethernet connection, and so on.

In some embodiments, memory 628 can include any suitable storage deviceor devices that can be used to store instructions, values, data, or thelike, that can be used, for example, by processor 622 to control the oneor more image acquisition systems 624, and/or receive data from the oneor more image acquisition systems 624; to images from data; presentcontent (e.g., images, a user interface) using a display; communicatewith one or more computing devices 550; and so on. Memory 628 caninclude any suitable volatile memory, non-volatile memory, storage, orany suitable combination thereof. For example, memory 628 can includeRAM, ROM, EEPROM, one or more flash drives, one or more hard disks, oneor more solid state drives, one or more optical drives, and so on. Insome embodiments, memory 628 can have encoded thereon, or otherwisestored therein, a program for controlling operation of image data source502. In such embodiments, processor 622 can execute at least a portionof the program to generate images, transmit information and/or content(e.g., data, images) to one or more computing devices 550, receiveinformation and/or content from one or more computing devices 550,receive instructions from one or more devices (e.g., a personalcomputer, a laptop computer, a tablet computer, a smartphone, etc.), andso on.

In some embodiments, any suitable computer readable media can be usedfor storing instructions for performing the functions and/or processesdescribed herein. For example, in some embodiments, computer readablemedia can be transitory or non-transitory. For example, non-transitorycomputer readable media can include media such as magnetic media (e.g.,hard disks, floppy disks), optical media (e.g., compact discs, digitalvideo discs, Blu-ray discs), semiconductor media (e.g., random accessmemory (“RAM”), flash memory, electrically programmable read only memory(“EPROM”), electrically erasable programmable read only memory(“EEPROM”)), any suitable media that is not fleeting or devoid of anysemblance of permanence during transmission, and/or any suitabletangible media. As another example, transitory computer readable mediacan include signals on networks, in wires, conductors, optical fibers,circuits, or any suitable media that is fleeting and devoid of anysemblance of permanence during transmission, and/or any suitableintangible media.

Referring particularly now to FIG. 7, an example of an MRI system 700that can implement the methods described here is illustrated. The MRIsystem 700 includes an operator workstation 702 that may include adisplay 704, one or more input devices 706 (e.g., a keyboard, a mouse),and a processor 708. The processor 708 may include a commerciallyavailable programmable machine running a commercially availableoperating system. The operator workstation 702 provides an operatorinterface that facilitates entering scan parameters into the MRI system700. The operator workstation 702 may be coupled to different servers,including, for example, a pulse sequence server 710, a data acquisitionserver 712, a data processing server 714, and a data store server 716.The operator workstation 702 and the servers 710, 712, 714, and 716 maybe connected via a communication system 740, which may include wired orwireless network connections.

The pulse sequence server 710 functions in response to instructionsprovided by the operator workstation 702 to operate a gradient system718 and a radiofrequency (“RF”) system 720. Gradient waveforms forperforming a prescribed scan are produced and applied to the gradientsystem 718, which then excites gradient coils in an assembly 722 toproduce the magnetic field gradients G_(x), G_(y), and G_(z) that areused for spatially encoding magnetic resonance signals. The gradientcoil assembly 722 forms part of a magnet assembly 724 that includes apolarizing magnet 726 and a whole-body RF coil 728.

RF waveforms are applied by the RF system 720 to the RF coil 728, or aseparate local coil to perform the prescribed magnetic resonance pulsesequence. Responsive magnetic resonance signals detected by the RF coil728, or a separate local coil, are received by the RF system 720. Theresponsive magnetic resonance signals may be amplified, demodulated,filtered, and digitized under direction of commands produced by thepulse sequence server 710. The RF system 720 includes an RF transmitterfor producing a wide variety of RF pulses used in MRI pulse sequences.The RF transmitter is responsive to the prescribed scan and directionfrom the pulse sequence server 710 to produce RF pulses of the desiredfrequency, phase, and pulse amplitude waveform. The generated RF pulsesmay be applied to the whole-body RF coil 728 or to one or more localcoils or coil arrays.

The RF system 720 also includes one or more RF receiver channels. An RFreceiver channel includes an RF preamplifier that amplifies the magneticresonance signal received by the coil 728 to which it is connected, anda detector that detects and digitizes the I and Q quadrature componentsof the received magnetic resonance signal. The magnitude of the receivedmagnetic resonance signal may, therefore, be determined at a sampledpoint by the square root of the sum of the squares of the I and Qcomponents:

M=√{right arrow over (I ² +Q ²)}  (1);

and the phase of the received magnetic resonance signal may also bedetermined according to the following relationship:

$\begin{matrix}{\phi = {{\tan^{- 1}\left( \frac{Q}{I} \right)}.}} & (2)\end{matrix}$

The pulse sequence server 710 may receive patient data from aphysiological acquisition controller 730. By way of example, thephysiological acquisition controller 730 may receive signals from anumber of different sensors connected to the patient, includingelectrocardiograph (“ECG”) signals from electrodes, or respiratorysignals from a respiratory bellows or other respiratory monitoringdevices. These signals may be used by the pulse sequence server 710 tosynchronize, or “gate,” the performance of the scan with the subject'sheart beat or respiration.

The pulse sequence server 710 may also connect to a scan room interfacecircuit 732 that receives signals from various sensors associated withthe condition of the patient and the magnet system. Through the scanroom interface circuit 732, a patient positioning system 734 can receivecommands to move the patient to desired positions during the scan.

The digitized magnetic resonance signal samples produced by the RFsystem 720 are received by the data acquisition server 712. The dataacquisition server 712 operates in response to instructions downloadedfrom the operator workstation 702 to receive the real-time magneticresonance data and provide buffer storage, so that data is not lost bydata overrun. In some scans, the data acquisition server 712 passes theacquired magnetic resonance data to the data processor server 714. Inscans that require information derived from acquired magnetic resonancedata to control the further performance of the scan, the dataacquisition server 712 may be programmed to produce such information andconvey it to the pulse sequence server 710. For example, duringpre-scans, magnetic resonance data may be acquired and used to calibratethe pulse sequence performed by the pulse sequence server 710. Asanother example, navigator signals may be acquired and used to adjustthe operating parameters of the RF system 720 or the gradient system718, or to control the view order in which k-space is sampled. In stillanother example, the data acquisition server 712 may also processmagnetic resonance signals used to detect the arrival of a contrastagent in a magnetic resonance angiography (“MRA”) scan. For example, thedata acquisition server 712 may acquire magnetic resonance data andprocesses it in real-time to produce information that is used to controlthe scan.

The data processing server 714 receives magnetic resonance data from thedata acquisition server 712 and processes the magnetic resonance data inaccordance with instructions provided by the operator workstation 702.Such processing may include, for example, reconstructing two-dimensionalor three-dimensional images by performing a Fourier transformation ofraw k-space data, performing other image reconstruction algorithms(e.g., iterative or backprojection reconstruction algorithms), applyingfilters to raw k-space data or to reconstructed images, generatingfunctional magnetic resonance images, or calculating motion or flowimages.

Images reconstructed by the data processing server 714 are conveyed backto the operator workstation 702 for storage. Real-time images may bestored in a data base memory cache, from which they may be output tooperator display 702 or a display 736. Batch mode images or selectedreal time images may be stored in a host database on disc storage 738.When such images have been reconstructed and transferred to storage, thedata processing server 714 may notify the data store server 716 on theoperator workstation 702. The operator workstation 702 may be used by anoperator to archive the images, produce films, or send the images via anetwork to other facilities.

The MRI system 700 may also include one or more networked workstations742. For example, a networked workstation 742 may include a display 744,one or more input devices 746 (e.g., a keyboard, a mouse), and aprocessor 748. The networked workstation 742 may be located within thesame facility as the operator workstation 702, or in a differentfacility, such as a different healthcare institution or clinic.

The networked workstation 742 may gain remote access to the dataprocessing server 714 or data store server 716 via the communicationsystem 740. Accordingly, multiple networked workstations 742 may haveaccess to the data processing server 714 and the data store server 716.In this manner, magnetic resonance data, reconstructed images, or otherdata may be exchanged between the data processing server 714 or the datastore server 716 and the networked workstations 742, such that the dataor images may be remotely processed by a networked workstation 742.

The present disclosure has described one or more preferred embodiments,and it should be appreciated that many equivalents, alternatives,variations, and modifications, aside from those expressly stated, arepossible and within the scope of the invention.

1. A method for generating an image that depicts a mechanical propertyin a tissue of a subject, the steps of the method comprising: (a)providing to a computer system, displacement data acquired with amagnetic resonance imaging (MRI) system and depicting displacementscaused in a subject by vibratory motion applied to the subject while thedata were acquired with the MRI system; (b) providing to the computersystem, training data representative of displacements caused byvibratory motion propagating in a medium; (c) constructing a neuralnetwork with the computer system; (d) training the neural network on thetraining data using the computer system; and (e) generating an imagethat depicts a mechanical property in a tissue of the subject byinputting the displacement data to the trained neural network. 2-11.(canceled)
 12. The method as recited in claim 1, wherein the trainingdata comprise simulated displacement data.
 13. The method as recited inclaim 12, wherein the simulated displacement data include dataindicative of simulated displacements caused by a single motion sourcein a volume.
 14. The method as recited in claim 12, wherein thesimulated displacement data include data indicative of simulateddisplacements caused by multiple motion sources in a volume.
 15. Themethod as recited in claim 12, wherein the simulated displacement datacomprise patches of simulated displacement data, wherein each patchcomprises a two-dimensional or three-dimensional array of voxels. 16.The method as recited in claim 12, wherein the training data comprisesimulated displacement data that simulates displacements in aninhomogeneous medium.
 17. The method as recited in claim 16, wherein thesimulated data are generated using a coupled harmonic oscillatorssimulation.
 18. The method as recited in claim 1, wherein the trainingdata include feature data comprising real and imaginary parts oftemporal harmonics of displacement data.
 19. The method as recited inclaim 18, wherein the feature data are scaled to a range of values. 20.The method as recited in claim 1, wherein the training data comprise atleast a portion of the displacement data acquired from the subject. 21.The method as recited in claim 1, wherein the neural network is afeedforward neural network.
 22. The method as recited in claim 1,wherein the neural network is a convolutional neural network. 23-26.(canceled)
 27. The method as recited in claim 1, wherein thedisplacement data comprises wave images that depict the vibratory motionin the subject.
 28. The method as recited in claim 1, wherein themechanical property is at least one of stiffness, storage modulus, lossmodulus, or damping ratio. 29-31. (canceled)
 32. The method as recitedin claim 1, wherein the mechanical property is a poroelastic parameter.33. The method as recited in claim 1, wherein the neural networkcomprises a variational sparse coding network.
 34. The method as recitedin claim 1, wherein the neural network comprises a convolutional sparsecoding network. 33-40. (canceled)
 41. The method as recited in claim 1,wherein the displacement data are representative of transientdisplacements.
 42. The method as recited in claim 1, wherein thedisplacement data comprise multiple frequency displacement data.
 43. Themethod as recited in claim 1, wherein the displacement data arerepresentative of multiple sources of displacements within the subject.